Awhile ago all of a sudden my PC just stopped booting - Would freeze at the Gigabyte splash screen, couldn't access BIOS or boot menu, followed by a blank screen with a flashing " - " in the top left corner where it would stay.

Tried clearing CMOS, making sure everything was plugged in right, all the usual troubleshooting.
RMA'd my motherboard - According to Gigabyte they couldn't find any trouble.
Put GPU and PSU in my mother's PC and it works fine.
I guess that leaves my CPU or RAM...waiting to receive my motherboard again to switch around the RAM and am going to order a case speaker to check for beep codes, but in the mean time does anyone have any ideas on what it could possibly be? I'm stumped.

Nope you are already on the way to proper troubleshooting. This should have been done before the board was sent in. Try 1 stick on memory at a time in different slots. If none of the memory you have works, borrow someone elses. If it post then your memory is dead.

IF it still will not post with test memory then you may have a cpu related issue. Remove all memory and power up. Do you hear beep codes? Is no the speaker isnt connected or your CPU is the cause. Make sure you have no power extensition cables in between psu and board. make sure 8 pin to board is plugged in. All else fails remove the heatsink. Power unit on while touching the top of the cpu. If it gets warm unplug it quickly. (means it is getting power). It it is cold then it is not getting power. either because of a short elsewhere in system or cpu is DOA.

I had the same issue with a Gigabyte 990FX board a while back. After serious amounts of troubleshooting and frustration, it turned out to be a bad SATA cable on the boot drive (one included with the board). Craziest thing, and only found this out entirely accidentally while troubleshooting.